Wstęp
Opis problemu
Problemem, który analizujemy w niniejszym projekcie jest wpływ poszczególnych czynników na wynik końcowy ucznia (?)
Baza danych
Baza danych którą analizujemy nazywa się „Wyniki uczniów”. Znajduje się w niej 20 kolumn z danymi oraz 6.608 wierszy danych. W bazie danych znajdują się zarówno zmienne liczbowe jak i jakościowe.
## Rows: 6,607
## Columns: 20
## $ Hours_Studied <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 23, 17,…
## $ Attendance <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 98, 80,…
## $ Parental_Involvement <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 8, 6, 8, 8, …
## $ Previous_Scores <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 71, 88,…
## $ Motivation_Level <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 0, 4, 2, 2, 2, 1…
## $ Family_Income <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 5, 4, 2, 4, 3, 4…
## $ Learning_Disabilities <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 72, 68,…
Czyszczenie danych
W niniejszym rozdziale sprawdzimy jakość danych, zbadamy występowanie braków danych oraz dobierzemy odpowiednią metodę imputacji brakujących danych (jeżeli zajdzie taka potrzeba).
Walidacja danych
Zostało wykonane badanie danych za pomocą funkcji aggr. Wykres po lewej stronie prezentuje proporcje braków danych. W naszym przypadku największe braki występują w trzech zmiennych:
- Sleep Hours - 5,22%
- Exam Score - 4,37%
- Distance from Home - 1,01%
Tabela po prawej stronie ilistruje współwystępowanie braków w zestawie danych. Czerwone pola oznaczają brakujące wartości. Można zauważyć, że brakujące dane są dość rozporoszone i nie występują jednocześnie w wielu zmiennych. Oznacza to, że nie instnieje współzależność pomiędzy występowaniem braków więc dane brakujące będziemy uzupełniać za pomocą podobieństwa.
aggr(czynniki, numbers = TRUE, sortVars = TRUE)
##
## Variables sorted by number of missings:
## Variable Count
## Sleep_Hours 0.05297412
## Family_Income 0.05297412
## Exam_Score 0.04540639
## Parental_Education_Level 0.01362192
## Teacher_Quality 0.01180566
## Distance_from_Home 0.01014076
## Hours_Studied 0.00000000
## Attendance 0.00000000
## Parental_Involvement 0.00000000
## Access_to_Resources 0.00000000
## Extracurricular_Activities 0.00000000
## Previous_Scores 0.00000000
## Motivation_Level 0.00000000
## Internet_Access 0.00000000
## Tutoring_Sessions 0.00000000
## School_Type 0.00000000
## Peer_Influence 0.00000000
## Physical_Activity 0.00000000
## Learning_Disabilities 0.00000000
## Gender 0.00000000
gg_miss_upset(czynniki)
Wykres poniżej został stworzony za pomocą funkcji gg_miss_upset. Prezentuje on wartości liczbowe brakujących danych
- Family income – 309
- Sleep Hours – 300
Z uwagi na stosunkowo wysoką ilość braków dokonamy imputacji danych.
czynniki1<- czynniki[!is.na(czynniki$Family_Income), ]
czynniki2<- czynniki1[!is.na(czynniki1$Parental_Education_Level), ]
czynniki3<- czynniki2[!is.na(czynniki2$Teacher_Quality), ]
czynniki4<- czynniki3[!is.na(czynniki3$Distance_from_Home), ]
unique(czynniki4$Family_Income)
## [1] "Low" "Medium" "High"
unique(czynniki4$Parental_Education_Level)
## [1] "High School" "College" "Postgraduate"
unique(czynniki4$Teacher_Quality)
## [1] "Medium" "High" "Low"
unique(czynniki4$Distance_from_Home)
## [1] "Near" "Moderate" "Far"
glimpse(czynniki4)
## Rows: 6,038
## Columns: 20
## $ Hours_Studied <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 17, 17,…
## $ Attendance <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 80, 97,…
## $ Parental_Involvement <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 6, 8, 8, NA,…
## $ Previous_Scores <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 88, 87,…
## $ Motivation_Level <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 4, 2, 2, 2, 1, 2…
## $ Family_Income <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 4, 2, 4, 3, 4, 4…
## $ Learning_Disabilities <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 68, 71,…
gg_miss_upset(czynniki4)
aggr(czynniki4, numbers = TRUE, sortVars = TRUE)
##
## Variables sorted by number of missings:
## Variable Count
## Sleep_Hours 0.05266645
## Exam_Score 0.04372309
## Hours_Studied 0.00000000
## Attendance 0.00000000
## Parental_Involvement 0.00000000
## Access_to_Resources 0.00000000
## Extracurricular_Activities 0.00000000
## Previous_Scores 0.00000000
## Motivation_Level 0.00000000
## Internet_Access 0.00000000
## Tutoring_Sessions 0.00000000
## Family_Income 0.00000000
## Teacher_Quality 0.00000000
## School_Type 0.00000000
## Peer_Influence 0.00000000
## Physical_Activity 0.00000000
## Learning_Disabilities 0.00000000
## Parental_Education_Level 0.00000000
## Distance_from_Home 0.00000000
## Gender 0.00000000
Imputacja danych
as.numeric(czynniki4$Exam_Score)
## [1] 67 61 74 71 NA 71 67 66 69 68 71 70 66 65 64 60 65 67
## [19] 66 69 72 66 66 63 65 71 66 64 69 67 68 61 64 67 63 NA
## [37] 67 65 64 70 68 65 68 64 68 63 64 67 67 66 72 65 71 66
## [55] 68 70 62 68 71 68 69 NA 69 65 70 71 65 72 69 66 68 65
## [73] 60 65 66 74 62 70 69 67 64 71 68 64 63 71 69 100 68 62
## [91] 68 66 64 67 65 65 69 63 72 76 69 67 69 63 67 66 79 64
## [109] 73 63 65 73 70 68 71 64 68 69 NA 67 68 64 66 63 66 66
## [127] 67 65 68 68 65 71 65 64 72 65 66 61 68 69 71 70 68 67
## [145] 68 68 72 65 66 65 67 NA 69 66 69 67 66 71 70 71 66 67
## [163] 66 72 68 69 71 70 67 69 65 65 64 63 69 64 72 63 64 64
## [181] 67 71 70 61 67 72 66 70 67 67 71 66 68 74 64 65 66 66
## [199] 68 78 67 74 74 62 66 69 68 89 66 68 67 75 60 66 73 68
## [217] 62 62 65 69 64 67 70 70 69 61 69 63 67 66 63 68 65 67
## [235] 68 64 71 69 67 65 68 67 67 66 70 65 69 65 63 67 61 65
## [253] 66 66 69 63 65 67 69 65 65 65 67 72 NA 65 69 68 64 59
## [271] 68 60 62 67 68 64 65 65 63 70 66 66 63 66 65 NA 67 66
## [289] 63 NA 67 71 67 69 67 72 70 67 64 67 69 63 68 70 66 68
## [307] 67 69 66 68 69 70 74 70 66 69 64 62 70 68 65 NA 71 66
## [325] 61 67 65 65 NA 62 60 61 67 70 69 66 64 68 67 64 65 66
## [343] 68 66 63 63 74 70 66 63 67 71 NA 72 68 66 70 66 72 61
## [361] 62 68 68 63 70 68 72 67 61 69 75 NA 65 75 64 70 67 63
## [379] 67 86 67 63 66 67 NA 66 64 73 68 70 67 62 68 72 69 66
## [397] 70 71 65 70 65 62 62 70 66 67 72 66 68 62 64 65 66 67
## [415] 69 68 64 68 64 71 61 68 64 72 NA 68 NA 66 63 74 63 72
## [433] 69 67 66 64 67 69 64 65 72 66 66 67 69 73 69 68 61 63
## [451] 68 63 65 68 66 66 70 61 71 70 69 61 68 74 67 70 64 66
## [469] 63 61 68 65 69 68 69 70 68 67 67 75 70 70 64 59 63 67
## [487] 68 68 97 66 61 70 65 64 69 64 61 64 68 67 62 66 72 71
## [505] 65 68 65 64 65 65 73 72 64 69 69 70 83 68 84 75 67 69
## [523] 66 65 70 66 74 68 68 62 71 63 69 71 66 64 65 69 66 67
## [541] 65 65 67 66 69 70 68 70 67 72 69 69 64 63 70 70 66 70
## [559] 66 68 61 NA 69 72 65 74 62 65 68 71 NA 65 68 70 63 63
## [577] 69 66 70 63 72 63 65 NA 80 68 64 73 66 66 66 59 68 67
## [595] 64 65 68 70 NA 72 62 68 73 69 67 65 63 66 66 70 69 70
## [613] 58 67 66 70 67 60 65 63 72 NA 70 70 64 64 72 66 66 71
## [631] 66 64 66 62 70 69 65 70 70 67 69 62 67 65 65 69 63 66
## [649] 67 69 67 70 67 70 65 63 NA 69 60 69 72 63 63 70 NA 69
## [667] 72 67 68 70 68 69 68 66 72 67 70 73 73 60 67 69 65 65
## [685] 64 67 65 64 67 70 63 71 68 67 67 68 66 68 70 67 67 62
## [703] 67 70 72 70 94 66 69 68 71 69 67 64 63 66 69 64 62 70
## [721] 67 68 62 68 64 64 66 72 72 66 NA 69 72 69 69 62 70 68
## [739] 68 70 65 73 66 71 62 68 70 68 70 72 69 63 62 68 69 68
## [757] 65 59 66 63 72 NA 94 70 66 69 64 63 71 65 68 64 64 67
## [775] 66 NA 66 71 71 68 64 67 64 68 62 64 68 69 65 67 71 65
## [793] 65 65 68 68 67 65 66 63 72 67 67 66 66 69 62 66 64 67
## [811] 71 68 66 75 72 68 68 69 63 70 66 66 71 72 69 71 69 68
## [829] NA 68 72 70 73 67 65 68 65 NA 66 67 70 NA 69 62 68 67
## [847] 68 69 62 75 65 63 66 71 66 NA 66 68 71 68 68 62 65 71
## [865] 63 68 69 69 71 71 62 NA 70 71 69 65 71 68 64 67 NA 71
## [883] 62 67 66 NA 65 64 65 68 72 64 62 69 64 61 72 66 69 65
## [901] 64 66 62 66 70 75 67 66 NA NA 72 65 67 63 62 69 70 63
## [919] 71 63 71 63 65 66 66 66 66 67 68 68 69 64 67 63 64 66
## [937] 65 68 66 71 74 65 68 68 72 NA 61 65 63 66 66 73 63 73
## [955] 63 65 65 66 65 70 68 64 68 62 61 69 65 65 NA 70 65 69
## [973] 65 69 65 72 70 64 67 69 70 65 69 74 66 72 75 70 63 65
## [991] 64 NA NA 67 67 68 65 61 63 80 69 NA 70 65 68 64 69 89
## [1009] 67 92 67 70 68 70 67 69 67 69 63 66 68 69 66 72 62 67
## [1027] 67 67 65 67 66 70 71 64 72 60 71 71 NA 74 64 68 66 64
## [1045] 65 69 63 65 62 67 64 61 65 70 59 75 67 64 72 76 69 65
## [1063] 72 69 71 64 74 68 66 65 67 69 66 67 64 67 NA 68 66 66
## [1081] 63 66 66 65 69 71 66 66 65 71 69 61 70 70 65 64 68 63
## [1099] 71 58 68 65 65 68 69 71 65 64 75 67 68 NA 67 72 69 68
## [1117] 70 69 63 61 66 73 67 72 69 69 63 67 63 66 62 68 65 59
## [1135] 72 63 68 61 65 68 61 67 66 75 68 65 NA 64 67 63 67 65
## [1153] 62 69 70 68 68 64 63 68 67 68 66 67 69 70 68 66 67 65
## [1171] 67 63 64 64 66 68 67 72 67 66 66 67 65 70 69 69 66 66
## [1189] 67 67 67 72 68 70 69 65 72 69 68 62 60 67 67 67 63 71
## [1207] 66 65 69 63 64 67 62 68 66 69 71 66 70 65 64 63 63 66
## [1225] 68 74 71 67 66 67 62 68 62 82 70 NA 64 66 68 64 61 69
## [1243] 64 67 67 65 68 67 64 70 69 66 69 66 73 66 69 70 71 70
## [1261] 69 63 NA 73 68 69 76 68 65 65 69 66 69 59 65 NA 64 69
## [1279] 70 67 67 NA 68 72 65 NA 75 65 63 71 66 69 68 71 77 70
## [1297] 66 NA NA NA 66 72 NA 63 72 71 72 65 67 68 66 71 70 68
## [1315] 72 66 65 62 69 65 69 69 75 70 74 65 63 74 67 71 68 69
## [1333] 71 66 65 66 65 67 70 63 64 71 68 72 71 64 64 66 68 65
## [1351] 67 64 70 65 65 68 61 69 64 69 67 NA 66 72 73 73 63 69
## [1369] 71 63 69 72 68 62 68 71 67 65 68 59 71 70 62 62 68 68
## [1387] 61 67 65 101 65 67 NA NA 64 67 69 67 62 66 72 67 66 67
## [1405] 67 68 63 NA 65 65 70 73 73 68 63 62 69 66 68 67 65 70
## [1423] 64 65 67 62 66 68 64 69 67 61 70 65 66 66 69 67 71 68
## [1441] 67 63 64 73 69 65 70 67 67 NA 69 68 NA 67 71 68 66 64
## [1459] 71 61 67 65 66 68 66 63 66 73 88 67 69 67 64 64 65 68
## [1477] 77 63 69 70 73 NA 71 66 71 66 63 70 66 66 66 62 69 63
## [1495] 68 NA 69 71 71 66 72 70 71 65 65 68 70 70 72 65 65 71
## [1513] 64 65 73 72 65 66 66 68 67 65 64 70 63 65 67 71 73 67
## [1531] 72 71 72 68 65 68 67 66 64 65 69 68 69 70 65 71 68 70
## [1549] 72 NA 64 NA NA 71 69 67 66 71 63 62 NA 66 72 67 65 66
## [1567] 68 69 68 61 68 64 67 68 61 66 64 67 64 72 62 63 70 69
## [1585] 64 66 67 71 70 69 64 70 69 60 65 67 66 68 58 67 62 69
## [1603] 73 66 67 71 NA 74 67 68 61 65 71 61 70 70 69 70 67 63
## [1621] 70 61 64 65 65 66 66 63 66 64 65 62 71 63 70 70 65 68
## [1639] 68 NA 71 68 67 72 68 60 68 NA 67 70 70 68 67 62 66 69
## [1657] 66 64 66 63 62 65 68 65 63 68 72 69 66 68 64 61 67 68
## [1675] 74 67 64 69 63 67 65 67 62 70 67 NA 65 69 64 74 64 64
## [1693] 67 63 68 66 68 68 69 71 65 67 65 65 80 74 59 69 66 66
## [1711] 65 67 69 68 73 71 67 67 66 63 65 NA 69 67 66 66 69 63
## [1729] 64 64 69 73 62 62 66 68 66 NA 62 NA 67 65 69 67 64 62
## [1747] 71 72 74 66 72 65 70 62 65 70 69 70 66 73 69 66 65 70
## [1765] 70 67 68 68 61 70 65 66 67 69 69 67 66 63 67 64 68 65
## [1783] 65 70 62 68 62 68 70 NA 73 68 68 69 63 74 61 69 64 63
## [1801] 68 72 69 70 63 62 72 69 66 71 62 68 63 66 NA 69 68 69
## [1819] 67 73 71 71 68 70 71 NA 63 71 69 71 68 68 66 67 59 66
## [1837] 64 NA 69 69 61 62 61 63 71 NA 68 67 70 64 71 71 67 63
## [1855] 66 70 70 67 69 66 67 65 72 68 72 76 65 68 65 66 63 63
## [1873] 66 72 64 67 66 68 65 71 62 69 65 70 70 70 69 NA 69 73
## [1891] 65 62 67 65 65 70 70 71 71 NA 65 84 68 70 68 67 69 68
## [1909] 59 67 NA 63 64 NA 66 67 66 66 68 66 68 65 67 64 59 60
## [1927] 65 66 65 69 62 60 68 64 73 64 63 65 65 67 66 65 66 66
## [1945] 70 71 70 68 NA 68 66 67 66 69 67 61 70 70 70 64 65 70
## [1963] 62 64 67 62 72 69 72 68 64 72 73 67 64 NA 67 68 71 NA
## [1981] 59 68 64 70 65 72 66 68 62 70 70 64 76 67 68 67 69 67
## [1999] 73 71 70 73 65 70 66 64 68 70 72 66 74 67 NA 60 69 71
## [2017] 66 65 60 69 69 67 65 70 71 73 70 67 67 65 68 74 68 61
## [2035] 67 66 69 62 71 71 72 69 67 NA 68 69 65 70 65 67 72 69
## [2053] 69 NA 67 65 70 63 71 64 69 69 70 64 70 74 69 73 66 67
## [2071] 76 61 68 63 67 66 62 67 66 63 64 67 66 68 NA 68 63 62
## [2089] 72 69 67 65 69 NA 70 91 65 62 65 NA 67 72 60 69 61 70
## [2107] 68 75 75 72 66 71 70 63 72 65 71 65 69 71 68 66 60 68
## [2125] 67 71 74 70 63 64 66 64 69 NA 64 65 69 68 68 68 65 65
## [2143] 66 66 71 68 65 63 66 71 65 68 66 64 70 70 71 70 70 66
## [2161] 64 66 68 61 72 66 68 61 67 66 74 66 67 71 66 71 72 66
## [2179] 62 66 69 69 69 64 68 63 64 69 71 67 66 67 NA 69 NA 66
## [2197] 63 67 66 66 67 66 69 72 60 68 72 64 65 76 59 67 NA 64
## [2215] 67 69 69 67 72 NA 62 69 68 99 70 68 67 66 66 62 72 68
## [2233] 66 68 75 67 65 68 67 67 73 67 71 67 68 68 NA 68 63 68
## [2251] 74 69 70 65 65 68 68 66 70 66 64 70 68 74 71 61 64 64
## [2269] 73 62 71 68 71 72 66 67 66 68 64 66 69 65 72 65 70 64
## [2287] 62 69 62 69 NA NA 64 63 69 68 NA 64 66 71 72 NA 66 65
## [2305] NA 62 68 65 62 74 NA 70 65 66 67 73 65 NA 66 67 58 71
## [2323] 63 73 NA 68 66 78 68 77 65 73 64 67 69 60 66 70 66 64
## [2341] 70 64 72 70 62 66 65 64 NA 71 68 68 65 64 75 61 68 NA
## [2359] 71 66 66 70 62 72 72 63 69 68 67 71 67 62 69 67 87 62
## [2377] 64 74 69 65 66 70 68 70 68 69 66 NA 71 66 61 NA 63 73
## [2395] 68 70 68 68 71 68 70 NA 69 73 72 67 69 68 64 71 68 70
## [2413] 72 65 70 69 64 67 65 62 68 68 68 68 NA 72 69 68 71 69
## [2431] 71 65 68 60 NA 66 66 62 61 69 69 74 62 67 69 66 NA 69
## [2449] 65 72 69 61 63 63 68 68 65 71 64 65 67 67 67 87 67 72
## [2467] 69 65 66 70 71 67 72 63 67 72 72 NA 67 68 70 67 69 74
## [2485] 63 72 71 69 62 NA 68 67 71 70 NA 60 69 71 NA 73 68 67
## [2503] 74 NA 69 69 68 66 69 68 65 71 61 63 66 69 71 73 72 73
## [2521] 65 71 65 67 69 63 68 70 64 64 68 65 66 70 66 69 64 64
## [2539] 69 67 63 67 65 64 68 64 70 70 69 70 65 70 63 74 70 66
## [2557] 68 67 66 66 69 67 69 66 64 61 61 70 65 67 69 63 66 73
## [2575] 68 74 70 68 67 65 66 64 72 70 60 68 71 68 67 70 65 60
## [2593] 65 70 69 64 67 NA 74 67 66 69 64 NA 66 65 67 67 68 65
## [2611] 66 65 71 63 70 70 67 68 63 70 69 66 70 68 70 67 64 62
## [2629] NA 62 66 64 72 NA 65 65 70 68 57 59 64 67 60 67 71 67
## [2647] 69 68 59 75 59 71 71 66 69 65 NA 68 88 66 67 63 68 65
## [2665] 67 67 67 64 65 70 67 68 65 63 72 68 71 70 68 68 68 71
## [2683] 70 67 61 64 67 65 66 62 70 64 70 66 62 63 66 58 70 63
## [2701] 65 NA 73 82 71 73 65 67 67 69 61 64 64 68 62 70 67 70
## [2719] 65 65 70 72 65 71 71 72 64 72 71 66 71 67 69 67 62 67
## [2737] NA NA 69 70 NA 65 66 68 72 65 60 63 73 71 59 70 63 67
## [2755] 65 64 71 NA 63 68 67 66 63 65 66 65 65 63 65 62 66 71
## [2773] 64 67 68 63 64 74 68 68 69 61 69 NA 67 63 68 68 67 69
## [2791] 64 67 70 72 NA 62 67 64 64 70 68 NA 65 59 69 67 68 62
## [2809] 65 69 65 68 68 71 71 66 66 66 65 66 67 66 69 66 64 70
## [2827] NA 67 60 66 72 63 69 NA 69 68 66 63 70 68 68 67 67 69
## [2845] 68 67 70 70 NA 61 68 64 66 73 66 65 68 69 72 63 65 69
## [2863] 62 66 69 67 94 71 66 71 66 60 60 66 67 67 64 66 68 70
## [2881] NA 86 73 61 68 70 71 71 68 70 70 62 67 68 68 64 69 70
## [2899] 73 66 68 68 66 62 67 73 65 70 68 67 66 65 66 66 60 NA
## [2917] 72 68 67 62 69 NA 64 65 75 69 65 60 69 65 67 70 66 69
## [2935] 69 68 70 66 65 65 65 69 69 65 NA 72 67 74 66 66 66 71
## [2953] 66 69 69 68 64 73 66 67 63 61 71 61 62 74 65 NA 66 76
## [2971] 67 71 65 68 68 67 64 60 73 69 70 64 64 65 62 72 64 67
## [2989] 64 61 72 70 70 71 68 68 70 73 69 71 64 NA 69 70 66 65
## [3007] 66 61 71 60 66 61 68 68 65 65 60 67 65 70 64 68 69 NA
## [3025] 65 65 68 66 65 71 68 62 61 70 62 65 68 70 68 69 73 71
## [3043] 63 66 67 66 69 72 NA 67 64 68 71 67 67 64 63 72 63 67
## [3061] 68 64 65 68 66 73 68 72 70 66 66 66 65 71 66 63 58 61
## [3079] 65 67 67 62 86 71 70 71 71 70 67 60 73 NA 62 67 61 61
## [3097] 60 68 65 67 67 74 64 64 67 74 69 62 69 68 74 68 73 70
## [3115] 68 64 71 65 68 67 NA 63 68 66 67 68 72 70 62 69 61 58
## [3133] 63 71 70 64 63 63 71 65 68 70 68 69 70 67 69 67 67 NA
## [3151] 63 67 70 71 74 70 59 64 67 63 66 62 65 73 70 62 NA 96
## [3169] 66 69 70 73 69 71 65 62 65 68 65 67 68 66 62 65 70 68
## [3187] 72 NA 63 67 69 NA 67 69 63 65 58 70 66 63 62 69 66 68
## [3205] 62 64 65 65 65 70 71 65 68 73 64 71 70 68 68 68 59 74
## [3223] 62 64 76 70 69 74 62 70 71 68 66 67 71 74 65 60 69 65
## [3241] 69 70 65 57 68 67 70 68 62 67 66 60 75 67 71 63 67 68
## [3259] 65 72 61 60 72 NA 67 71 66 70 64 66 NA 67 67 64 61 99
## [3277] NA 72 66 64 69 65 66 73 66 65 71 58 69 63 66 69 69 63
## [3295] 65 76 67 70 60 68 68 68 69 62 64 71 68 72 64 73 69 70
## [3313] 69 64 66 69 NA 65 62 75 60 63 66 67 68 72 66 63 71 67
## [3331] NA 66 68 66 68 68 66 66 70 68 65 70 66 68 64 65 NA 66
## [3349] 68 70 65 65 68 67 72 70 72 71 64 69 NA 70 68 71 71 NA
## [3367] 68 70 72 66 65 66 65 72 68 68 67 68 67 NA 65 70 64 66
## [3385] 64 66 67 68 71 67 69 67 61 68 67 64 63 72 69 66 64 61
## [3403] 63 65 71 78 65 66 66 74 62 66 71 67 69 72 72 65 71 64
## [3421] 69 65 69 64 69 68 NA 66 66 67 62 66 68 68 63 66 72 70
## [3439] 63 65 65 66 68 64 66 68 64 62 67 65 59 66 NA 63 68 66
## [3457] NA 66 69 64 68 66 68 62 68 69 70 65 68 67 64 66 67 63
## [3475] 69 70 70 65 NA 67 61 70 68 64 68 68 65 69 63 69 61 69
## [3493] 62 58 71 NA 68 61 67 72 71 67 68 64 73 65 67 63 63 69
## [3511] 68 68 69 73 66 68 65 67 70 64 69 71 68 68 66 70 65 NA
## [3529] 70 67 63 64 60 62 65 69 66 72 68 69 65 65 70 67 73 70
## [3547] 66 68 61 70 66 67 69 64 65 75 63 69 68 66 66 66 68 65
## [3565] 70 68 70 61 64 71 72 66 63 62 66 72 68 NA 70 73 67 65
## [3583] NA 65 70 66 65 68 66 71 65 70 69 67 82 66 66 65 61 72
## [3601] 70 71 84 72 70 62 71 62 68 74 68 NA 65 66 68 67 63 71
## [3619] 63 66 67 66 70 71 68 64 66 72 68 70 64 71 72 71 63 68
## [3637] 63 66 NA NA 70 65 67 66 69 73 66 70 68 65 67 71 70 61
## [3655] 69 63 67 65 63 67 66 72 68 67 NA 66 73 71 65 65 65 68
## [3673] 70 NA 62 66 65 71 61 63 67 70 73 69 61 64 61 63 65 NA
## [3691] 68 72 62 58 68 74 68 67 65 63 71 62 65 66 71 68 72 66
## [3709] 66 67 71 72 64 60 NA 68 62 68 60 72 65 63 66 65 65 67
## [3727] 65 67 66 71 64 61 65 61 69 71 70 62 73 66 66 66 66 65
## [3745] 67 76 66 63 71 63 63 66 72 70 62 69 66 64 NA 67 71 69
## [3763] 70 70 61 NA 67 70 68 69 65 68 67 70 68 69 70 67 70 74
## [3781] 63 72 62 71 68 72 64 64 63 66 71 70 67 73 64 65 62 64
## [3799] 67 74 63 64 64 70 71 63 65 70 65 68 72 67 65 66 67 65
## [3817] 68 68 69 71 64 64 67 70 66 70 70 64 71 63 72 72 63 67
## [3835] 67 64 69 NA 71 70 98 65 63 61 67 64 65 73 69 67 NA 67
## [3853] 66 64 68 66 65 65 67 68 63 70 68 NA NA 69 65 61 65 67
## [3871] 66 69 NA 68 65 64 68 64 70 68 NA 61 66 75 71 69 62 65
## [3889] 61 69 66 64 69 78 68 68 68 69 68 80 NA 64 64 68 65 66
## [3907] 67 64 66 63 71 62 64 72 NA 67 65 63 65 67 67 64 69 60
## [3925] 70 66 66 68 72 64 64 64 72 66 68 95 64 NA 68 67 67 71
## [3943] 63 66 65 68 68 62 67 NA 71 71 61 70 NA 70 67 66 63 65
## [3961] 75 66 61 65 61 73 63 67 62 71 70 70 69 66 72 63 65 71
## [3979] 66 69 62 66 66 64 68 68 67 68 65 NA 85 64 68 NA 65 63
## [3997] 64 62 68 63 68 63 68 62 67 66 65 69 64 75 66 62 70 NA
## [4015] 66 65 68 68 62 66 68 69 67 74 61 64 69 66 61 71 71 69
## [4033] 66 68 71 66 94 68 66 70 68 64 69 59 70 72 64 63 67 62
## [4051] 69 66 66 63 62 58 67 68 67 67 62 66 65 67 69 67 69 62
## [4069] 67 63 66 71 68 67 71 65 64 69 68 67 71 64 NA 69 67 58
## [4087] 66 69 70 70 70 66 61 71 NA 69 74 71 68 69 63 67 NA 66
## [4105] 69 68 63 69 66 71 68 69 65 68 67 65 65 64 69 64 66 65
## [4123] 69 66 64 61 72 67 63 69 70 71 60 70 69 63 69 71 68 64
## [4141] 68 69 65 68 74 72 67 73 68 70 62 67 69 93 68 69 68 64
## [4159] 69 66 68 72 63 NA 65 65 68 70 65 66 66 NA 64 66 63 68
## [4177] 68 65 69 66 72 NA 67 68 71 73 68 69 69 63 62 70 66 62
## [4195] 64 63 71 67 67 67 71 93 72 71 63 65 61 66 61 67 64 69
## [4213] 70 73 63 64 69 69 67 62 66 68 71 66 NA 68 59 70 66 65
## [4231] 66 73 65 65 NA 74 68 65 72 71 69 67 71 68 69 68 73 69
## [4249] 58 65 58 66 NA 67 67 65 71 66 68 65 71 NA 72 69 70 66
## [4267] NA 62 66 70 73 70 71 NA 64 66 82 68 67 68 69 63 66 68
## [4285] 71 69 70 70 NA 68 65 72 67 68 69 70 69 68 65 70 65 61
## [4303] 69 67 65 63 67 76 70 67 66 65 65 63 72 68 62 65 69 61
## [4321] 67 66 70 72 69 68 74 70 67 68 69 66 68 69 66 NA 66 64
## [4339] 63 68 65 65 68 62 67 73 69 65 66 73 72 72 61 69 66 74
## [4357] 66 66 72 70 67 71 63 NA 64 65 65 62 65 64 NA 67 66 NA
## [4375] 68 58 65 68 64 66 92 69 68 63 64 68 67 68 66 68 64 63
## [4393] 62 66 65 66 66 69 67 NA 73 66 61 NA 67 66 69 69 67 65
## [4411] 63 63 66 66 69 72 70 68 66 67 68 62 64 71 65 69 65 71
## [4429] 69 65 66 68 72 74 64 64 63 66 67 64 62 71 63 72 71 61
## [4447] 71 69 61 68 67 70 69 72 66 67 70 68 68 65 63 62 66 62
## [4465] 61 63 64 74 70 68 69 62 71 69 68 65 65 72 63 72 66 71
## [4483] 67 61 70 68 70 65 65 65 65 66 62 63 63 70 67 66 63 66
## [4501] 67 68 67 66 71 69 72 70 68 68 67 62 67 69 64 66 69 70
## [4519] 69 72 61 NA 68 NA 65 66 67 68 67 63 64 66 69 70 72 63
## [4537] 68 67 69 69 71 67 64 68 67 62 68 72 61 67 70 59 70 60
## [4555] 74 68 67 67 63 62 64 68 65 71 68 68 68 67 NA 70 69 70
## [4573] 69 59 64 70 63 66 72 71 62 62 64 65 68 67 61 68 68 62
## [4591] 62 74 68 66 65 66 67 76 66 68 63 65 63 59 74 62 59 71
## [4609] 73 68 68 66 69 70 74 75 71 71 65 NA 65 67 67 71 72 62
## [4627] 70 72 64 66 69 71 68 71 66 68 61 71 70 66 61 67 72 65
## [4645] 68 70 63 69 62 71 64 71 72 66 69 60 68 65 67 66 68 63
## [4663] NA 66 67 66 60 67 NA 70 69 68 67 63 70 71 67 64 66 70
## [4681] 65 68 65 65 69 70 64 62 73 62 62 72 67 68 65 79 66 68
## [4699] 65 67 67 68 72 65 65 70 68 63 68 69 NA 64 69 62 65 70
## [4717] 72 66 70 67 65 68 68 69 72 65 63 68 62 69 65 65 70 59
## [4735] 63 64 63 67 65 64 65 72 72 66 62 68 67 69 67 63 65 71
## [4753] 70 68 65 68 69 NA 62 72 64 58 66 64 68 69 71 71 62 70
## [4771] 63 66 65 69 63 64 66 67 66 65 72 70 67 72 65 62 67 64
## [4789] 72 66 70 66 67 NA 72 68 64 66 68 66 NA 70 69 69 66 68
## [4807] 71 64 67 68 68 69 71 68 65 63 65 72 67 69 67 64 62 71
## [4825] 64 69 65 73 64 64 70 70 64 74 69 67 73 66 67 75 73 67
## [4843] 65 71 63 68 72 NA 67 66 72 64 68 65 74 65 63 65 70 71
## [4861] 66 NA 67 64 67 NA 70 71 68 65 70 67 63 65 70 67 60 65
## [4879] 64 67 71 69 70 69 63 67 66 69 69 72 65 63 69 69 64 69
## [4897] 72 62 66 65 65 67 63 66 61 64 65 68 69 61 72 61 66 60
## [4915] 69 72 69 71 64 71 64 67 67 66 73 73 70 70 62 68 65 73
## [4933] 66 64 63 62 70 NA 64 70 62 67 66 74 69 70 68 71 73 69
## [4951] 61 68 66 67 64 67 61 62 69 61 69 64 65 64 68 67 68 61
## [4969] 69 64 74 66 68 65 66 66 65 67 65 63 67 70 68 66 NA 72
## [4987] 68 66 62 67 62 67 68 66 68 62 68 62 69 62 71 69 66 64
## [5005] 65 NA 69 68 71 66 65 72 67 67 70 64 65 68 67 66 69 64
## [5023] 68 68 65 65 65 67 63 62 73 72 71 67 66 68 70 66 56 71
## [5041] 64 NA 70 70 71 70 62 72 62 67 NA 60 72 66 66 69 70 70
## [5059] 70 67 67 59 68 71 61 63 67 70 69 66 70 67 61 74 70 66
## [5077] 73 65 64 63 69 NA 65 NA 69 71 68 70 71 68 69 71 63 66
## [5095] 67 71 59 66 72 70 68 63 69 75 67 74 66 65 60 63 69 68
## [5113] 65 74 65 61 67 66 69 65 65 66 73 64 67 67 68 71 64 67
## [5131] 68 67 70 64 63 71 64 70 70 67 62 NA 69 NA 70 69 65 66
## [5149] 69 66 65 66 72 62 64 61 70 67 66 66 68 67 65 70 68 61
## [5167] 65 71 66 61 67 66 71 62 67 64 68 67 63 70 67 71 62 75
## [5185] 72 73 64 66 69 70 70 71 64 71 63 68 71 66 72 65 60 67
## [5203] 65 64 72 62 67 67 69 65 62 69 72 63 64 67 70 64 69 72
## [5221] 69 75 67 67 64 68 65 70 57 69 70 63 66 64 62 71 64 72
## [5239] 64 71 68 68 68 69 67 66 65 63 62 67 65 66 64 67 67 61
## [5257] 66 66 67 64 67 68 64 63 68 64 70 64 59 71 67 73 66 73
## [5275] 62 69 66 NA 65 67 64 67 66 NA 68 64 63 72 75 71 66 71
## [5293] NA NA 58 62 69 65 69 68 70 72 66 68 67 61 64 74 64 64
## [5311] 61 71 72 68 69 74 70 69 64 71 65 71 66 64 NA 71 65 59
## [5329] 63 64 63 70 70 NA 65 71 70 66 64 64 59 65 NA 67 62 70
## [5347] 75 66 65 64 70 71 68 64 67 65 62 68 66 68 NA 68 66 70
## [5365] 60 69 65 NA 64 71 66 66 68 NA 66 61 70 68 65 69 67 62
## [5383] 61 65 65 66 NA 69 70 63 64 65 71 61 69 69 66 72 60 62
## [5401] 66 69 69 71 57 72 66 70 67 65 68 63 63 68 60 67 65 68
## [5419] 62 65 66 67 60 74 62 61 NA 66 NA 72 70 71 64 70 68 61
## [5437] 68 64 64 NA 72 66 74 65 64 69 62 62 72 73 64 65 70 66
## [5455] 70 69 64 63 66 68 97 71 66 72 70 69 66 69 65 75 70 70
## [5473] 69 73 74 66 74 67 67 70 67 80 70 71 64 68 68 69 72 65
## [5491] 64 64 58 69 61 68 66 68 70 62 71 61 NA 65 63 74 68 65
## [5509] 66 69 69 70 70 71 72 61 68 66 70 NA 62 69 69 64 63 69
## [5527] 61 70 64 76 73 69 72 70 73 68 66 67 67 62 72 65 69 69
## [5545] 69 69 69 70 67 69 75 66 63 64 66 72 71 70 67 65 65 73
## [5563] 66 NA 71 66 65 75 74 65 71 65 65 67 66 67 66 65 59 63
## [5581] 65 61 68 65 72 59 63 69 70 67 66 68 71 69 66 66 74 66
## [5599] 72 69 68 71 61 65 71 59 71 72 71 67 67 74 63 68 NA 66
## [5617] 67 70 65 68 70 66 69 65 68 65 70 NA NA 64 70 64 67 68
## [5635] 67 66 66 67 NA NA 68 67 69 64 67 67 67 67 68 65 70 68
## [5653] 72 67 66 68 75 66 67 71 68 65 67 66 60 NA 64 72 60 NA
## [5671] 62 70 65 77 71 66 74 70 NA 64 NA 68 63 61 61 65 69 69
## [5689] 65 72 69 71 67 72 70 68 66 68 71 70 65 65 68 69 66 62
## [5707] 70 65 71 68 65 70 69 66 67 63 70 65 70 74 68 64 73 66
## [5725] 66 67 67 69 69 68 64 70 67 68 67 73 65 69 63 68 64 68
## [5743] 66 65 69 69 74 64 63 64 71 NA 72 67 64 70 65 69 65 66
## [5761] 67 68 65 68 63 65 61 68 65 66 65 NA 70 70 67 75 65 66
## [5779] 62 64 60 70 72 67 67 72 63 60 NA 72 70 71 66 NA 73 71
## [5797] 64 66 69 66 63 62 98 71 66 75 68 69 68 60 64 71 69 60
## [5815] 70 66 68 67 69 75 65 65 66 64 70 63 66 71 68 68 71 63
## [5833] NA 73 68 70 66 72 70 68 60 68 74 68 72 69 98 68 70 64
## [5851] 65 67 65 70 68 65 74 65 68 74 67 64 66 61 73 70 70 63
## [5869] 69 NA 68 65 68 69 66 58 67 65 62 65 69 70 70 63 69 64
## [5887] 69 70 64 65 70 60 68 61 68 61 64 66 70 65 74 66 65 69
## [5905] 69 66 63 69 65 67 67 65 69 NA 67 66 64 70 65 65 64 64
## [5923] 61 65 68 70 74 60 71 70 67 68 64 67 65 72 65 71 72 70
## [5941] 63 67 67 62 72 69 61 67 66 68 62 63 70 68 71 65 59 64
## [5959] 67 68 95 70 68 65 NA 67 69 68 72 71 75 70 66 67 70 71
## [5977] 64 65 64 62 64 66 64 71 NA 70 71 68 66 66 65 64 67 65
## [5995] 69 69 69 68 67 68 65 69 73 76 69 69 68 70 NA 73 64 65
## [6013] 62 64 69 67 65 63 66 70 70 67 65 66 66 72 64 71 70 64
## [6031] 70 67 NA 68 69 68 68 64
as.numeric(czynniki4$Sleep_Hours)
## [1] 7 8 7 8 6 8 NA 6 6 8 6 8 8 NA 8 10 6 9 7 5 6 8 8 5
## [25] 6 6 4 4 7 8 5 6 7 9 8 6 8 6 7 7 9 8 6 6 7 5 7 8
## [49] 8 7 5 5 6 8 8 7 10 9 8 8 NA 4 5 7 7 7 7 4 8 7 7 8
## [73] 7 7 6 4 5 7 7 7 6 5 7 7 8 6 4 4 6 7 7 6 5 4 NA 7
## [97] 6 5 6 7 7 7 9 6 9 7 7 8 6 7 5 8 8 9 9 6 8 6 7 10
## [121] 8 8 6 7 NA 9 7 NA 5 9 6 8 6 8 NA 9 8 6 8 8 5 5 5 5
## [145] 8 8 4 6 5 8 6 5 7 8 6 7 6 9 6 6 7 7 8 9 9 6 7 NA
## [169] 9 6 8 8 8 9 NA 6 8 7 4 5 8 8 5 9 7 5 6 NA 6 4 7 8
## [193] 5 7 6 8 4 8 4 7 6 NA 5 9 5 5 10 7 5 7 4 6 7 9 7 7
## [217] 6 9 8 8 7 5 9 7 7 8 7 5 7 7 9 4 7 8 NA 6 5 6 9 4
## [241] 5 6 6 7 9 5 7 7 6 5 6 6 8 8 5 6 6 10 7 5 6 6 8 7
## [265] 7 7 7 4 7 5 10 7 7 6 8 5 7 6 8 6 9 8 8 9 6 8 4 7
## [289] 6 5 6 6 7 6 7 6 6 7 7 8 8 8 7 7 8 6 4 5 9 7 7 7
## [313] 8 NA 7 8 6 8 NA 7 6 7 6 9 4 8 8 6 8 7 5 9 8 8 6 8
## [337] 5 4 5 NA 6 6 6 4 7 NA 6 9 7 8 NA 8 7 5 6 7 4 NA 10 8
## [361] 8 7 8 9 8 7 7 8 6 8 6 5 6 10 6 NA 6 7 4 5 6 5 7 5
## [385] 7 NA 7 6 9 8 NA 6 8 9 8 5 NA 8 7 6 7 7 NA 8 6 7 9 7
## [409] 8 5 8 8 6 7 7 8 6 7 9 9 8 NA 9 7 7 6 8 8 7 5 8 6
## [433] 7 9 5 7 NA 7 7 8 7 8 7 7 NA 7 6 8 7 6 9 7 5 7 7 7
## [457] 6 NA 10 4 5 6 6 5 6 7 5 8 5 8 8 6 5 8 6 NA 8 6 7 6
## [481] 9 6 7 8 7 8 7 5 7 NA 7 9 4 8 6 6 9 7 6 8 NA 9 10 8
## [505] 7 5 9 NA 8 8 7 NA 10 7 6 9 7 7 9 8 8 NA 5 6 7 7 8 8
## [529] 5 10 7 9 4 7 5 6 7 6 9 10 6 NA 5 9 7 7 7 8 5 7 6 7
## [553] 8 6 9 4 9 9 6 6 5 8 7 5 NA 6 7 7 6 6 8 NA 9 6 4 6
## [577] 6 5 7 7 4 7 9 8 7 4 6 9 6 6 5 7 7 6 10 8 7 4 8 10
## [601] 7 6 5 8 9 6 6 7 6 5 6 6 9 9 8 NA 6 9 8 5 6 5 4 NA
## [625] 5 6 6 9 5 5 8 6 6 5 8 7 7 6 6 7 8 9 9 8 8 6 8 7
## [649] 8 8 8 5 7 6 6 NA 7 4 8 9 8 7 9 6 7 10 5 5 8 7 6 5
## [673] 4 5 9 7 4 9 9 9 6 7 7 8 9 7 8 7 7 6 5 6 6 NA 9 7
## [697] 6 8 7 8 6 9 9 7 8 9 6 7 7 5 8 9 7 8 9 6 6 6 8 8
## [721] 7 8 9 8 7 7 8 7 8 9 7 4 10 7 9 10 9 7 10 9 NA 6 4 8
## [745] 9 8 4 5 10 7 9 5 7 7 6 10 7 5 5 8 6 6 8 4 6 5 6 7
## [769] 7 7 9 7 NA 10 7 10 7 7 NA 7 9 10 4 NA 6 4 8 8 8 8 7 8
## [793] 7 7 7 5 8 5 NA 7 5 6 6 9 7 8 9 9 7 6 8 NA 8 7 8 7
## [817] 6 8 7 10 6 8 6 4 8 6 9 8 7 5 8 6 5 8 5 4 9 6 4 6
## [841] 6 9 5 5 8 6 NA 6 NA NA 7 9 6 6 8 9 6 7 8 9 8 6 10 NA
## [865] 7 8 8 10 7 7 9 7 NA 8 8 4 4 NA 7 7 7 8 8 8 NA 7 7 9
## [889] 6 7 7 9 4 7 8 10 7 6 10 8 9 8 5 5 8 8 6 9 6 7 7 9
## [913] 5 6 5 10 7 6 NA 8 8 6 5 7 9 NA 6 5 8 10 8 6 6 10 6 7
## [937] 7 8 9 9 7 7 8 6 NA 7 8 10 8 7 6 7 5 4 8 8 NA 7 4 8
## [961] 9 8 7 NA 6 7 7 6 7 NA 10 7 6 NA 9 9 10 7 8 5 6 5 8 7
## [985] 7 6 4 7 7 4 8 7 8 10 7 8 9 8 6 5 8 6 9 6 7 5 6 6
## [1009] 6 7 6 10 NA 9 7 7 6 10 7 6 NA NA 9 6 6 9 10 7 9 5 6 NA
## [1033] 8 7 9 6 7 5 9 9 8 7 6 7 8 NA 9 9 6 7 6 6 9 7 7 7
## [1057] 7 6 NA 6 6 7 NA 6 8 7 7 8 4 6 8 7 7 6 9 8 NA 9 6 8
## [1081] 8 7 7 9 6 9 6 7 6 10 7 5 7 8 7 6 9 5 6 7 6 8 10 6
## [1105] 9 5 8 6 8 4 5 8 6 7 10 NA 8 6 7 5 6 7 7 8 8 5 6 4
## [1129] 6 8 9 7 9 8 7 6 4 9 NA 9 NA 7 6 7 7 7 6 6 9 6 4 5
## [1153] NA 7 6 9 8 10 6 7 9 8 6 8 8 6 7 9 8 6 6 8 4 6 9 7
## [1177] 6 5 8 7 7 8 7 7 5 5 8 8 8 6 8 6 NA 6 6 NA 8 7 7 6
## [1201] 7 7 6 7 7 10 6 6 7 6 5 5 6 6 7 4 8 6 8 8 6 NA 9 5
## [1225] 8 NA 9 6 6 NA 8 6 7 6 5 7 6 6 9 6 NA 9 6 7 8 8 10 6
## [1249] 5 8 7 7 6 6 NA 6 7 NA 5 5 6 9 6 5 6 5 8 5 NA 7 8 8
## [1273] 5 9 7 10 9 7 10 7 10 8 8 NA NA 8 7 7 NA 8 8 6 7 4 8 10
## [1297] 7 5 8 6 8 8 NA 7 8 7 6 8 5 7 5 6 6 9 9 9 6 8 7 7
## [1321] 4 8 7 8 8 6 7 5 9 8 6 8 7 6 7 8 8 10 7 NA 8 7 6 6
## [1345] 4 8 5 6 7 10 5 10 9 8 9 8 4 6 7 6 8 7 8 7 7 6 5 7
## [1369] 6 9 5 10 7 NA 6 8 7 7 8 9 6 7 7 10 7 8 8 8 6 6 7 4
## [1393] 7 6 7 7 5 NA 8 7 8 5 9 8 7 NA 9 6 5 6 7 7 9 6 6 5
## [1417] 8 5 8 6 6 10 9 7 5 10 7 7 8 4 7 7 5 7 7 10 9 7 7 9
## [1441] 7 5 10 6 10 8 6 NA 8 5 8 10 5 6 9 7 7 9 8 6 10 5 7 6
## [1465] NA 5 7 8 9 9 7 6 9 6 5 8 9 6 8 8 6 9 5 6 6 5 8 8
## [1489] 8 7 8 7 6 6 4 9 9 10 6 6 NA 8 9 6 8 9 8 5 7 4 5 5
## [1513] 7 7 7 5 7 8 8 8 8 8 8 5 5 6 NA 7 7 4 7 7 4 7 5 6
## [1537] 8 7 6 6 6 7 5 9 5 8 6 7 8 6 7 8 9 6 6 8 7 7 9 4
## [1561] 5 4 9 8 5 7 NA 4 7 5 8 5 7 9 8 8 7 5 6 7 7 5 8 5
## [1585] 9 7 8 8 10 7 6 9 5 7 7 8 5 7 7 5 7 7 6 6 5 8 9 10
## [1609] 8 6 6 7 7 7 9 6 9 7 6 6 7 8 6 8 6 7 5 8 NA 9 8 7
## [1633] 9 8 9 6 8 9 5 5 4 5 6 8 7 6 5 7 8 8 10 NA 7 7 7 6
## [1657] 4 5 8 7 8 8 8 8 7 7 4 6 6 7 6 8 6 NA 6 6 6 6 9 7
## [1681] 7 6 7 7 7 9 7 5 7 6 8 7 9 6 7 5 7 5 7 7 7 8 7 5
## [1705] 6 7 7 7 9 7 8 4 NA 10 9 NA 10 7 7 7 NA 4 8 7 7 7 9 8
## [1729] 7 7 6 7 8 7 7 8 5 6 5 7 8 9 9 6 7 6 9 9 7 6 4 5
## [1753] 5 10 5 6 10 7 8 7 4 9 8 7 10 6 7 NA NA 8 7 5 6 5 9 5
## [1777] 9 9 6 6 6 9 9 6 9 9 7 7 9 9 8 7 9 10 6 7 8 8 6 9
## [1801] 6 6 6 5 8 7 9 8 4 9 10 9 9 NA 6 7 8 8 6 6 5 8 6 7
## [1825] 10 8 7 8 9 5 6 7 6 7 5 8 6 NA 7 8 4 8 7 8 5 8 9 7
## [1849] 6 6 8 8 8 7 NA 7 6 8 7 9 9 7 8 6 7 8 5 8 6 6 6 7
## [1873] 5 7 7 6 5 8 5 10 8 8 7 6 6 5 7 9 5 9 NA 8 8 7 7 6
## [1897] 7 7 NA 8 7 7 6 6 8 6 6 6 6 9 7 7 7 5 9 8 8 8 10 6
## [1921] 5 8 5 7 7 8 6 6 8 6 7 9 7 9 7 6 8 4 8 6 8 7 5 6
## [1945] 7 7 8 8 8 8 NA 10 8 8 10 7 6 9 9 7 10 7 8 9 7 9 6 6
## [1969] 9 7 6 7 8 5 8 8 9 7 7 7 7 10 5 8 7 7 8 9 8 9 7 7
## [1993] 5 10 7 8 9 6 9 7 9 8 7 5 8 4 8 7 4 6 6 NA 9 9 6 6
## [2017] NA 7 6 6 6 6 9 8 8 9 8 9 8 7 8 7 5 4 10 6 6 9 5 8
## [2041] 10 10 6 7 6 7 9 5 8 7 9 9 6 7 8 8 4 8 9 7 8 9 7 8
## [2065] 7 7 6 7 10 6 NA 7 9 9 6 6 6 6 NA 6 6 NA 7 7 6 5 9 7
## [2089] 10 8 10 8 7 6 6 9 7 8 8 8 6 9 7 7 8 7 4 9 9 4 5 10
## [2113] 7 7 6 5 7 8 7 8 NA 6 7 9 6 7 10 6 9 7 10 5 7 5 6 6
## [2137] 7 5 NA 8 5 6 10 7 4 5 7 7 NA 10 10 7 8 8 9 6 8 7 7 7
## [2161] 5 4 7 6 8 8 7 9 7 5 7 9 4 7 8 10 9 7 8 4 5 7 7 7
## [2185] 7 7 5 7 5 6 7 8 7 6 5 6 7 8 8 5 8 5 8 8 4 8 NA 9
## [2209] 6 7 8 8 8 6 8 8 7 6 6 9 8 7 7 4 7 5 7 9 NA 7 8 6
## [2233] 7 8 NA 7 9 8 5 5 4 5 7 9 6 8 4 NA 6 10 4 4 6 4 6 7
## [2257] 7 5 9 8 8 5 9 9 7 8 7 NA 7 6 7 9 6 6 NA 7 8 8 7 10
## [2281] 7 8 10 8 6 7 7 NA 6 9 8 7 NA 7 8 10 4 8 7 7 4 8 7 6
## [2305] 7 7 4 7 8 6 7 9 7 8 7 10 6 6 7 6 5 8 NA 6 5 4 8 5
## [2329] 7 8 8 5 NA 9 6 6 8 5 7 8 5 6 9 7 8 8 7 5 6 7 5 5
## [2353] 9 NA NA 8 6 4 6 7 7 7 7 6 8 5 8 6 10 7 6 6 6 8 8 8
## [2377] 7 8 9 8 7 8 5 10 8 8 7 4 7 7 6 6 8 9 7 6 7 7 8 6
## [2401] 8 8 6 4 6 9 4 9 4 6 6 NA 7 7 6 8 NA 7 6 8 8 6 6 6
## [2425] 7 8 7 4 8 5 6 7 7 8 6 6 7 NA 8 7 9 9 8 5 8 7 6 6
## [2449] 7 6 7 7 8 7 6 4 8 7 7 9 5 7 NA 8 4 NA 8 6 7 6 NA 8
## [2473] 5 5 9 10 8 8 7 7 7 9 7 7 7 9 7 7 6 5 9 9 9 5 9 10
## [2497] 9 9 8 8 5 6 7 7 8 4 7 8 8 8 8 8 7 6 NA 8 10 8 8 5
## [2521] 7 7 8 8 8 10 NA 8 8 10 8 8 8 9 6 10 4 7 7 7 9 8 6 6
## [2545] 7 9 7 7 8 7 9 7 7 NA 8 7 NA 10 8 NA 7 7 8 4 4 9 7 6
## [2569] 5 7 7 9 8 7 8 9 8 8 7 6 5 5 8 8 9 8 9 7 NA 5 7 4
## [2593] 7 9 7 8 7 6 7 9 8 6 5 7 6 7 5 9 7 7 6 7 7 6 7 9
## [2617] 4 7 6 9 7 5 7 8 10 4 9 5 7 NA 7 7 9 8 7 7 8 9 8 9
## [2641] 6 9 8 6 7 7 7 NA 6 7 6 6 9 7 10 7 9 7 7 8 NA 7 7 6
## [2665] 7 8 7 7 7 7 8 7 7 8 7 7 7 5 7 10 6 6 10 NA 9 7 7 8
## [2689] 7 NA 4 NA NA 10 8 NA 9 6 6 4 6 8 9 5 7 4 7 10 4 NA 8 8
## [2713] 6 9 6 8 9 8 8 8 9 7 6 7 6 6 9 8 8 9 8 10 4 6 7 7
## [2737] 10 8 6 8 4 7 7 6 7 6 6 8 8 6 6 6 7 6 9 7 8 5 6 8
## [2761] 8 5 7 7 6 8 5 6 8 7 7 7 8 8 8 7 6 6 5 6 6 9 5 9
## [2785] 7 7 8 5 6 5 6 NA 9 6 4 6 8 9 7 6 7 8 5 7 7 7 7 6
## [2809] 8 7 7 5 8 6 9 5 4 4 4 8 7 9 7 7 7 6 6 5 8 7 7 10
## [2833] 6 7 7 9 7 7 10 6 7 8 6 8 6 NA 8 7 5 NA 7 8 7 8 8 7
## [2857] 7 7 6 NA 8 9 6 8 9 9 5 NA 4 5 9 6 5 9 5 9 5 5 7 6
## [2881] 7 10 7 9 7 NA 4 8 8 6 10 6 5 8 5 7 8 NA 6 9 5 8 8 7
## [2905] 7 6 6 7 8 9 4 4 9 7 7 7 10 8 6 6 NA NA 9 6 5 9 5 8
## [2929] 6 9 5 6 8 8 9 8 8 9 5 6 5 4 8 9 8 8 7 7 10 9 6 9
## [2953] 9 8 8 5 5 5 NA 6 8 8 8 6 7 8 8 6 7 7 6 NA 6 7 6 6
## [2977] 8 6 NA 8 7 7 7 8 7 7 5 7 9 6 5 8 8 6 7 7 NA 8 6 8
## [3001] 6 9 10 6 8 7 8 6 7 6 7 5 7 5 NA 7 8 8 8 5 9 6 6 7
## [3025] 8 8 6 7 7 8 6 6 5 NA 8 9 NA 4 7 10 6 7 5 7 7 5 5 5
## [3049] 6 8 6 9 6 7 8 9 6 8 6 10 5 8 9 5 8 6 10 4 5 5 5 NA
## [3073] 10 9 7 6 8 7 6 5 7 7 6 6 8 8 10 NA 5 7 5 NA 10 9 9 9
## [3097] 4 8 6 8 10 9 7 9 4 8 8 8 8 8 4 7 6 8 6 NA 5 7 7 8
## [3121] 7 9 7 NA 7 NA 5 5 9 6 7 7 NA 9 7 6 6 8 8 8 7 5 8 7
## [3145] 7 5 6 8 7 8 9 8 8 6 6 9 6 8 10 8 7 5 7 9 7 9 8 7
## [3169] 5 6 6 8 7 9 7 6 6 7 6 9 7 6 5 7 8 6 7 8 7 5 5 4
## [3193] 8 5 7 6 6 6 6 9 6 8 9 NA 8 6 7 6 7 5 8 5 7 6 8 7
## [3217] 5 8 7 7 10 9 7 5 5 9 6 5 8 9 9 6 8 7 8 7 6 9 7 6
## [3241] 7 6 8 7 6 10 5 8 7 5 6 5 7 7 10 6 9 8 4 6 8 NA 6 6
## [3265] 7 10 6 7 8 5 5 5 5 9 8 8 8 7 7 NA 5 10 NA 6 7 10 9 8
## [3289] 8 6 8 7 NA 9 7 5 6 8 9 8 8 7 7 7 7 6 8 NA 5 6 8 8
## [3313] 4 8 7 6 7 5 7 5 6 6 8 NA 8 NA 7 8 9 5 6 8 9 7 5 7
## [3337] 8 7 5 9 6 8 4 NA 6 8 5 7 9 6 9 8 9 7 7 10 8 7 8 6
## [3361] 7 9 7 6 6 7 6 5 5 9 7 7 6 6 6 7 5 9 7 7 8 8 6 8
## [3385] 8 7 9 8 NA 9 7 7 8 7 8 6 4 8 5 NA 8 NA 4 7 7 8 5 NA
## [3409] 8 6 10 6 7 5 7 4 7 9 5 5 9 5 10 8 9 6 9 NA 8 6 5 7
## [3433] 7 6 9 10 7 6 10 8 8 9 7 7 9 8 6 6 9 9 10 6 7 6 NA 7
## [3457] 8 6 4 5 7 10 6 7 8 6 6 7 6 4 6 9 9 6 6 6 7 6 7 NA
## [3481] 8 6 6 8 8 7 8 10 8 10 7 9 9 7 6 6 8 5 6 8 4 5 10 9
## [3505] 6 5 5 8 10 10 5 7 6 NA 5 6 6 8 6 8 9 10 8 7 9 9 8 5
## [3529] 9 8 6 6 8 4 7 6 6 5 9 4 7 6 10 7 4 8 5 8 8 9 7 8
## [3553] 7 6 9 5 7 6 8 NA 6 7 9 6 6 5 6 7 7 10 4 10 9 7 6 7
## [3577] 10 6 7 6 6 6 5 7 7 6 4 7 7 7 8 6 9 8 8 10 6 9 9 7
## [3601] 10 7 7 7 8 NA 10 6 4 10 9 8 6 8 5 7 7 8 5 NA 7 8 7 6
## [3625] 4 5 6 5 8 7 10 10 9 6 9 4 9 4 7 9 8 5 7 8 7 6 8 NA
## [3649] 7 9 NA 6 9 9 6 6 10 7 7 7 9 10 7 10 6 7 8 6 NA 6 5 4
## [3673] 7 8 5 7 7 7 6 7 7 8 5 5 7 6 7 6 9 9 8 8 7 7 10 6
## [3697] 5 NA 5 5 7 8 5 6 8 6 6 5 6 6 7 8 7 7 8 6 8 5 7 9
## [3721] 7 9 7 10 4 8 4 7 9 9 8 7 8 10 8 6 8 6 8 8 8 7 9 6
## [3745] 7 7 9 6 7 6 8 5 9 8 6 6 9 8 6 6 8 8 8 7 8 7 6 9
## [3769] NA 7 7 6 7 6 8 7 5 7 6 4 7 9 7 8 7 6 6 5 8 8 7 4
## [3793] 8 6 7 5 7 7 4 9 7 7 8 NA 8 5 4 7 9 5 6 4 7 8 8 6
## [3817] 4 5 9 8 NA 5 9 6 8 5 7 9 6 8 5 6 8 NA 8 6 5 6 9 6
## [3841] 9 7 10 10 9 5 4 7 8 8 6 5 8 10 6 10 7 7 8 7 9 6 7 5
## [3865] NA 5 8 5 8 6 10 9 8 5 NA 6 6 9 6 6 6 8 5 7 8 4 5 7
## [3889] 9 9 6 9 7 7 7 6 6 5 8 8 8 5 6 9 7 7 8 7 NA 8 5 9
## [3913] 6 8 7 6 NA 8 7 10 8 NA 9 8 9 6 NA 7 9 10 6 7 8 7 6 6
## [3937] 8 7 7 7 6 7 6 6 5 7 8 9 5 9 7 5 6 4 5 10 6 8 7 7
## [3961] 8 4 9 7 6 8 7 7 8 7 5 8 7 4 NA 6 8 6 5 9 8 7 8 8
## [3985] 5 7 9 7 8 7 9 9 9 10 8 8 6 6 7 5 7 8 5 7 7 7 8 8
## [4009] 9 8 9 7 7 7 9 7 7 10 5 8 7 7 6 6 6 8 8 4 5 8 8 5
## [4033] NA 8 6 5 7 7 7 6 10 6 6 7 NA 8 9 8 4 NA 9 9 8 6 7 6
## [4057] 5 NA 10 6 9 6 5 8 7 9 9 7 9 6 9 5 9 9 6 9 5 6 7 8
## [4081] 5 10 4 7 4 9 6 7 7 5 5 9 7 4 7 4 7 6 7 8 9 5 6 8
## [4105] 7 4 7 9 5 7 4 8 7 6 6 5 9 6 8 6 NA 9 10 10 6 6 10 7
## [4129] NA 6 6 8 4 8 8 6 7 7 7 8 6 10 7 7 10 4 10 7 6 5 6 7
## [4153] 8 7 6 9 10 9 6 8 8 NA 6 6 9 8 5 8 10 6 6 8 9 7 9 6
## [4177] 5 6 5 8 6 7 NA 7 7 9 5 8 8 7 6 5 10 7 7 10 7 10 5 NA
## [4201] 5 7 6 7 6 7 6 9 5 7 5 6 7 7 5 6 5 9 5 10 9 8 7 8
## [4225] 8 9 7 9 7 10 7 5 7 8 NA 4 8 8 5 7 7 8 6 6 5 10 8 6
## [4249] 5 5 7 4 8 8 7 7 8 7 8 5 8 7 9 7 7 6 9 4 8 7 7 7
## [4273] 8 6 7 8 6 8 8 6 5 6 7 7 9 6 6 8 6 6 6 4 8 8 NA 10
## [4297] 9 6 9 7 6 6 NA 7 9 NA 6 5 8 8 9 7 8 8 7 8 8 7 10 10
## [4321] 7 7 NA 7 9 5 7 8 9 5 6 6 5 7 NA 7 5 4 8 6 5 8 6 4
## [4345] 7 9 6 6 10 8 10 7 7 9 7 7 10 7 8 6 8 7 8 7 8 5 9 6
## [4369] NA 6 7 7 8 8 8 8 7 7 8 5 4 NA 7 8 6 9 8 NA 4 NA 9 7
## [4393] 7 7 NA 9 6 8 7 8 6 9 8 NA 5 5 10 NA 6 8 6 4 4 7 9 9
## [4417] 9 8 NA 9 4 8 5 6 8 8 6 8 8 7 7 10 7 7 NA 7 8 9 7 6
## [4441] 10 4 10 9 9 9 10 NA 6 6 NA 6 5 6 7 9 NA 8 5 4 NA 6 NA 6
## [4465] 6 6 5 4 4 7 9 7 7 5 6 NA 4 9 4 7 8 9 6 10 7 7 7 10
## [4489] NA 6 9 8 5 5 7 8 6 4 5 9 8 9 9 6 6 7 8 9 10 NA 8 10
## [4513] 7 9 8 NA 7 5 8 8 6 7 6 6 6 5 6 8 9 10 6 9 8 7 8 NA
## [4537] NA 6 6 6 6 7 7 6 10 6 7 4 7 5 6 4 6 NA 7 6 7 6 7 7
## [4561] 7 NA 8 8 7 7 7 7 7 6 4 7 8 5 NA 8 NA 7 9 9 6 8 6 10
## [4585] 7 5 8 9 9 7 8 6 8 8 5 7 7 7 7 9 NA 4 10 4 8 5 9 7
## [4609] 8 4 8 8 8 8 7 7 6 6 NA 6 4 6 7 8 4 4 7 9 4 8 9 NA
## [4633] 8 7 10 6 7 6 7 7 9 9 8 9 6 6 8 7 10 4 8 6 6 5 9 NA
## [4657] 6 6 5 5 6 9 10 6 6 5 8 8 7 6 9 8 8 NA 7 6 8 8 8 5
## [4681] 8 7 6 8 7 8 7 7 9 5 6 6 7 6 6 7 9 NA 8 NA 6 4 8 8
## [4705] 7 6 6 8 8 8 8 8 8 6 5 7 8 5 7 9 NA 9 7 NA 6 7 5 5
## [4729] NA 7 10 7 7 9 6 4 6 6 4 7 6 5 8 7 7 8 7 NA 6 5 7 6
## [4753] 8 7 8 6 5 10 7 8 NA 7 9 5 10 7 6 6 7 8 7 8 8 7 6 7
## [4777] 10 7 9 6 7 NA NA 5 9 10 6 6 7 6 5 9 6 7 5 8 7 4 9 8
## [4801] 7 7 10 8 7 5 7 8 7 6 6 8 6 4 NA 7 8 8 5 7 6 6 6 7
## [4825] 10 6 7 7 7 NA 7 6 9 5 8 6 4 6 6 5 8 5 6 7 6 6 6 6
## [4849] 8 6 7 9 8 5 8 9 6 5 6 7 8 6 4 5 8 10 7 9 5 6 4 6
## [4873] 8 6 10 10 4 6 8 5 9 9 5 7 7 8 7 8 5 9 9 7 NA NA 7 NA
## [4897] 7 7 5 5 10 7 7 9 8 8 5 7 6 6 7 8 7 9 9 9 7 6 7 9
## [4921] 9 4 7 4 7 6 6 8 6 7 6 7 6 8 7 7 6 8 8 7 7 8 8 7
## [4945] 9 8 10 8 9 9 7 5 9 6 7 10 5 6 6 7 8 8 NA 6 5 6 8 7
## [4969] 4 4 7 8 6 8 5 7 7 8 5 5 NA 5 NA 9 NA 8 8 8 7 10 7 8
## [4993] 6 6 9 6 8 8 7 4 9 6 7 5 6 6 7 6 10 7 8 8 6 6 6 8
## [5017] 8 7 7 10 7 4 8 8 9 8 6 NA 7 9 9 NA 8 9 7 10 9 6 7 8
## [5041] 10 8 7 9 7 6 8 6 10 NA 8 9 7 7 7 5 7 8 5 9 7 7 5 6
## [5065] 5 6 7 8 4 7 7 6 6 9 10 4 6 7 8 7 7 8 8 8 7 7 8 7
## [5089] 8 6 8 9 5 5 8 7 NA 8 6 8 8 6 9 7 5 5 8 5 5 8 5 8
## [5113] 8 4 8 5 6 9 6 7 6 6 5 7 7 8 7 NA 8 6 5 8 6 7 6 6
## [5137] 4 8 4 9 9 6 NA 10 7 7 9 5 7 8 8 7 7 7 8 7 7 6 10 6
## [5161] 8 10 5 8 10 6 6 7 6 10 7 6 6 8 8 NA 5 7 7 6 9 8 7 6
## [5185] 10 5 6 7 8 5 6 8 NA 6 7 6 7 7 9 8 7 7 10 6 7 6 8 10
## [5209] 7 7 7 5 7 10 8 9 9 6 10 4 7 4 4 8 9 4 7 9 10 NA 5 5
## [5233] 7 10 6 NA 5 7 NA 7 8 8 7 7 7 7 6 5 7 6 NA 7 8 5 10 4
## [5257] 9 7 6 5 7 7 9 7 7 8 7 7 7 8 6 6 8 5 7 6 8 9 6 8
## [5281] 7 6 7 9 7 9 7 5 7 7 6 10 9 7 9 NA 5 8 8 6 6 8 4 8
## [5305] 7 NA 8 6 5 9 7 7 8 6 8 8 9 9 7 8 NA 7 7 4 9 8 7 7
## [5329] 6 6 8 5 5 8 7 7 7 10 7 7 10 7 10 NA 5 10 6 8 10 9 6 8
## [5353] 8 6 8 6 7 5 NA 7 5 8 8 8 9 8 7 7 10 8 7 7 NA 5 10 8
## [5377] 5 7 9 6 6 NA 8 6 8 NA 6 7 8 6 8 9 6 10 9 7 NA 6 NA 7
## [5401] 5 4 7 7 6 5 4 6 8 7 8 8 8 5 6 10 4 7 8 4 6 10 7 6
## [5425] NA 6 10 6 6 5 7 7 9 NA 8 7 4 6 6 10 8 7 4 4 8 8 6 7
## [5449] 7 7 6 8 9 6 5 7 8 8 8 8 7 7 8 7 7 7 9 7 6 6 8 6
## [5473] 7 NA 5 5 6 5 8 10 6 6 6 8 8 7 5 6 7 7 7 8 5 7 7 6
## [5497] 6 8 5 10 8 7 7 8 6 6 9 6 7 6 7 8 10 6 5 7 6 NA 8 10
## [5521] 4 7 8 7 7 8 7 8 4 6 6 7 6 8 7 5 NA 8 7 NA 8 6 9 9
## [5545] 4 7 6 7 6 6 8 5 7 5 9 7 8 7 7 7 9 6 4 6 5 8 7 8
## [5569] 7 NA NA 9 7 9 7 7 6 9 6 7 5 NA 9 8 10 7 9 8 7 8 6 4
## [5593] 6 4 4 8 8 8 8 4 9 8 8 10 8 5 8 5 7 7 5 5 7 9 8 8
## [5617] 5 7 10 7 9 9 8 7 6 7 6 7 5 NA 6 6 6 7 4 6 7 8 NA 6
## [5641] 7 8 9 NA 6 6 9 6 5 7 9 6 6 6 8 7 9 5 6 6 7 8 6 6
## [5665] 8 8 4 7 7 6 6 6 4 6 5 7 5 8 5 9 8 5 7 6 8 10 6 7
## [5689] 9 8 9 8 7 7 5 6 6 6 7 7 NA 8 9 NA NA 8 8 8 9 8 9 7
## [5713] 6 9 10 9 7 9 8 5 7 7 9 7 6 8 4 6 8 7 8 7 7 6 8 5
## [5737] 7 9 6 5 4 NA 8 6 5 7 5 9 4 5 7 8 9 8 9 7 6 9 9 8
## [5761] NA 9 8 7 8 8 8 7 6 9 6 7 NA 9 7 9 10 7 8 8 7 8 8 NA
## [5785] 10 7 9 9 4 9 9 7 8 8 9 6 9 5 4 8 9 7 4 5 8 7 9 7
## [5809] 6 7 9 9 7 7 8 6 8 7 7 7 10 6 6 9 8 5 7 8 6 8 7 6
## [5833] 9 9 7 8 9 6 8 6 5 6 5 8 6 5 8 8 7 6 6 9 6 6 8 8
## [5857] 7 9 6 8 9 6 6 7 7 8 7 7 6 7 9 9 4 6 7 7 7 6 6 6
## [5881] 8 8 6 9 8 6 7 8 5 5 8 6 9 10 8 8 5 5 7 5 7 6 7 7
## [5905] 7 6 5 7 4 9 8 6 8 6 7 6 7 5 7 5 10 NA 7 8 5 6 8 7
## [5929] 6 8 7 8 8 6 7 6 8 8 6 NA 9 7 8 7 7 7 6 7 4 6 8 8
## [5953] NA 8 8 7 6 8 7 6 6 7 9 7 7 8 8 7 NA 6 9 6 9 7 7 8
## [5977] 6 8 7 8 6 6 4 6 6 6 7 8 8 8 NA 7 7 8 8 5 7 4 4 6
## [6001] 7 6 4 8 6 8 6 6 8 6 7 7 8 6 8 5 8 8 7 NA 7 8 6 7
## [6025] 8 8 10 7 NA 6 5 NA 6 7 8 6 6 9
czynniki5 <- hotdeck(czynniki4)
miss_var_summary(czynniki5)
## # A tibble: 40 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Hours_Studied 0 0
## 2 Attendance 0 0
## 3 Parental_Involvement 0 0
## 4 Access_to_Resources 0 0
## 5 Extracurricular_Activities 0 0
## 6 Sleep_Hours 0 0
## 7 Previous_Scores 0 0
## 8 Motivation_Level 0 0
## 9 Internet_Access 0 0
## 10 Tutoring_Sessions 0 0
## # ℹ 30 more rows
Reguły walidacyjne
rules <- validator(
Hours_Studied >= 0,
Hours_Studied <= 168,
Attendance >= 0,
Attendance <= 100,
Sleep_Hours >= 0,
Sleep_Hours <= 24,
Previous_Scores >= 0,
Previous_Scores <= 100,
Physical_Activity >= 0,
Physical_Activity <= 168,
Exam_Score >= 0,
Exam_Score <= 100,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity >= 0,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity <= 168
)
wyniki <- confront(czynniki5, rules)
summary(wyniki)
## name items passes fails nNA error warning
## 1 V01 6038 6038 0 0 FALSE FALSE
## 2 V02 6038 6038 0 0 FALSE FALSE
## 3 V03 6038 6038 0 0 FALSE FALSE
## 4 V04 6038 6038 0 0 FALSE FALSE
## 5 V05 6038 6038 0 0 FALSE FALSE
## 6 V06 6038 6038 0 0 FALSE FALSE
## 7 V07 6038 6038 0 0 FALSE FALSE
## 8 V08 6038 6038 0 0 FALSE FALSE
## 9 V09 6038 6038 0 0 FALSE FALSE
## 10 V10 6038 6038 0 0 FALSE FALSE
## 11 V11 6038 6038 0 0 FALSE FALSE
## 12 V12 6038 6037 1 0 FALSE FALSE
## 13 V13 6038 6038 0 0 FALSE FALSE
## 14 V14 6038 6038 0 0 FALSE FALSE
## expression
## 1 Hours_Studied - 0 >= -1e-08
## 2 Hours_Studied - 168 <= 1e-08
## 3 Attendance - 0 >= -1e-08
## 4 Attendance - 100 <= 1e-08
## 5 Sleep_Hours - 0 >= -1e-08
## 6 Sleep_Hours - 24 <= 1e-08
## 7 Previous_Scores - 0 >= -1e-08
## 8 Previous_Scores - 100 <= 1e-08
## 9 Physical_Activity - 0 >= -1e-08
## 10 Physical_Activity - 168 <= 1e-08
## 11 Exam_Score - 0 >= -1e-08
## 12 Exam_Score - 100 <= 1e-08
## 13 Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 0 >= -1e-08
## 14 Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 168 <= 1e-08
plot(wyniki)
dane_zwalidowane <- czynniki5 %>%
replace_errors(rules)
errors_removed(dane_zwalidowane)
## call: locate_errors(data, x, ref, ..., cl = cl, Ncpus = Ncpus)
## located 1 error(s).
## located 0 missing value(s).
## Use 'summary', 'values', '$errors' or '$weight', to explore and retrieve the errors.
par(mfrow=c(2,3))
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied")
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")
par(mfrow=c(2,3)) #zmienić przy kolejnych wykresach na c(1,1) bo będzie pamiętać i tworzyć wykresy w blokach 6- wykresowych
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied")
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")
ggplot(dane_zwalidowane, aes(x=Attendance)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Hours_Studied)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Sleep_Hours)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Previous_Scores)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Tutoring_Sessions)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Exam_Score)) +
geom_boxplot() +
theme_bw() +
coord_flip()
grubbs.test(dane_zwalidowane$Hours_Studied)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Hours_Studied
## G = 4.01539, U = 0.99733, p-value = 0.1773
## alternative hypothesis: highest value 44 is an outlier
grubbs.test(dane_zwalidowane$Attendance)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Attendance
## G = 1.72722, U = 0.99951, p-value = 1
## alternative hypothesis: lowest value 60 is an outlier
grubbs.test(dane_zwalidowane$Sleep_Hours)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Sleep_Hours
## G = 2.0532, U = 0.9993, p-value = 1
## alternative hypothesis: lowest value 4 is an outlier
grubbs.test(dane_zwalidowane$Previous_Scores)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Previous_Scores
## G = 1.7435, U = 0.9995, p-value = 1
## alternative hypothesis: lowest value 50 is an outlier
grubbs.test(dane_zwalidowane$Tutoring_Sessions)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Tutoring_Sessions
## G = 5.25143, U = 0.99543, p-value = 0.0004415
## alternative hypothesis: highest value 8 is an outlier
grubbs.test(dane_zwalidowane$Exam_Score)
##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Exam_Score
## G = 8.38735, U = 0.98834, p-value < 2.2e-16
## alternative hypothesis: highest value 100 is an outlier
ggplot(dane_zwalidowane, aes(x = Gender, fill = Gender))+
geom_bar()+
scale_fill_manual(values =c("Female"="pink","Male"="lightblue"))+
theme_minimal()+
ggtitle("Podział płci w próbie")+
theme(plot.title = element_text(hjust =0.5))
ggplot(dane_zwalidowane, aes(x = Exam_Score, fill = Exam_Score))+
geom_histogram(binwidth =5,fill="#5C1C81", color ="black")+
theme_minimal()+
ggtitle("Rozkład wyników egzaminów")+
theme(plot.title = element_text(hjust =0.5))
w1 <- ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
facet_grid(~Gender)
w2 <-ggplot(dane_zwalidowane, aes(x = Hours_Studied))+
geom_histogram(binwidth =5, fill ="darkgreen", color ="black")+
theme_minimal()+
labs(title ="Rozkład godzin nauki", x ="Godziny nauki w tygodniu", y="Liczba uczniów")+
facet_grid(~Gender)
grid.arrange(w1, w2, nrow = 1)
ggplot(dane_zwalidowane, aes(x = Hours_Studied, y = Exam_Score))+
geom_point(color ="blue", alpha =0.6)+
geom_smooth(method ="lm", color ="red", se =FALSE)+
theme_minimal()+
labs(title ="Relacja między godzinami nauki a wynikiem egzaminu",
x ="Godziny nauki w tygodniu",
y ="Wynik egzaminu")
## `geom_smooth()` using formula = 'y ~ x'
ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
geom_violin()+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od zaangażowania rodziców",
x ="Zaangażowanie rodziców",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set2")
# Wykres słupkowy typów szkół
ggplot(dane_zwalidowane, aes(x = School_Type, fill = School_Type))+
geom_bar()+
theme_minimal()+
labs(title ="Rozkład typów szkół",
x ="Typ szkoły",
y ="Liczba uczniów")+
scale_fill_brewer(palette ="Set1")
ggplot(dane_zwalidowane, aes(x = School_Type, y = Exam_Score, fill = School_Type))+
geom_boxplot()+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od typów szkół",
x ="Typ Szkoły",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set2")
ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
geom_boxplot()+
facet_wrap(~ Motivation_Level)+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od motywacji i zaangażowania rodziców",
x ="Zaangażowanie rodziców",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set3")
ggplot(dane_zwalidowane, aes(x = Access_to_Resources, y = Exam_Score, fill = Access_to_Resources))+
geom_boxplot()+
facet_wrap(~ Internet_Access)+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od dostępu do źródeł i internetu",
x ="Dostęp do źródeł",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set5")
ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
facet_grid(~Learning_Disabilities)
# Wykres heksagonalny
ggplot(dane_zwalidowane, aes(x = Distance_from_Home, y = Exam_Score)) +
geom_hex(bins = 30) + # Liczba przedziałów (możesz dostosować np. 20, 40)
scale_fill_viridis_c() + # Kolorystyka dla lepszej wizualizacji
theme_minimal() +
labs(
title = "Zależność między wynikiem egzaminu a dystansem od domu",
x = "Dystans od domu do szkoły",
y = "Wynik Egzaminu",
fill = "Gęstość"
)
ld_counts <- dane_zwalidowane %>%
count(Learning_Disabilities)%>%
mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Learning_Disabilities))+
geom_bar(stat ="identity", width =1)+
coord_polar("y", start =0)+
scale_fill_manual(values =c("Yes"="red","No"="lightblue"))+
theme_void()+
ggtitle("Udział osób z trudnościami w uczeniu się")+
theme(plot.title = element_text(hjust =0.5))+
geom_text(aes(label = paste0(Percentage,"%")),
position = position_stack(vjust =0.5),
color ="black", size =5)
ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="darkred", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Poziom wykształcenia rodziców")+
facet_grid(~Parental_Education_Level)
# Upewniamy się, że kategorie są w poprawnej kolejności
dane_zwalidowane$Teacher_Quality <- factor(dane_zwalidowane$Teacher_Quality, levels =c("Low","Medium","High"))# Obliczenie mediany wyników egzaminów dla każdej kategorii jakości nauczycieli
median_scores <- dane_zwalidowane %>%
group_by(Teacher_Quality)%>%
summarise(Median_Exam_Score = median(Exam_Score, na.rm =TRUE))# Wykres liniowy z medianą
ggplot(median_scores, aes(x = Teacher_Quality, y = Median_Exam_Score, group =1))+
geom_line(color ="#ff6347", size =1)+# Linia wykresu
geom_point(color ="darkred", size =3)+# Punkty oznaczające medianę
geom_text(aes(label =round(Median_Exam_Score,1)), vjust =-1)+# Etykiety mediany
ylim(0,100)+# Skala od 0 do 100
theme_minimal()+
ggtitle("Mediana wyniku egzaminu a jakość nauczycieli")+
xlab("Jakość nauczycieli")+
ylab("Mediana wyniku egzaminu")+
theme(plot.title = element_text(hjust =0.5))
ggplot(dane_zwalidowane, aes(x = Family_Income, y = Tutoring_Sessions, color = Family_Income)) +
geom_jitter(width = 0.2, alpha = 0.7) + # Dodanie punktów z małym zakłóceniem na osi X (w celu uniknięcia nakładania punktów)
geom_smooth(method = "lm", se = FALSE, color = "black") + # Linia trendu (regresji liniowej)
scale_color_manual(values = c("High" = "lightgreen", "Medium" = "lightblue", "Low" = "lightpink")) +
theme_minimal() +
labs(
title = "Wpływ dochodów rodziny na liczbę korepetycji",
x = "Dochód rodziny",
y = "Liczba korepetycji",
color = "Dochód"
)
## `geom_smooth()` using formula = 'y ~ x'
ld_counts <- dane_zwalidowane %>%
count(Family_Income)%>%
mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Family_Income))+
geom_bar(stat ="identity", width =1)+
coord_polar("y", start =0)+
scale_fill_manual(values =c("Low"="lightpink","Medium"="lightblue","High"="lightgreen"))+
theme_void()+
ggtitle("Poziom dochodów rodziców")+
theme(plot.title = element_text(hjust =0.5))+
geom_text(aes(label = paste0(Percentage,"%")),
position = position_stack(vjust =0.5),
color ="black", size =5)
ggplot(dane_zwalidowane, aes(x = Sleep_Hours, y = Exam_Score)) +
geom_jitter(color = "purple", alpha = 0.5) +
geom_smooth(method = "lm", color = "orange", se = TRUE) +
theme_minimal() +
labs(title = "Relacja między godzinami snu a wynikiem egzaminu",
x = "Godziny snu",
y = "Wynik egzaminu")
## `geom_smooth()` using formula = 'y ~ x'
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Hours_Studied
stat_desc <- data %>%
summarise(
średnia = mean(Hours_Studied, na.rm = TRUE),
mediana = median(Hours_Studied, na.rm = TRUE),
odchylenie_standardowe = sd(Hours_Studied, na.rm = TRUE),
minimum = min(Hours_Studied, na.rm = TRUE),
maksimum = max(Hours_Studied, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Hours_Studied"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Hours_Studied | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 19.99 |
| mediana | 20.00 |
| odchylenie_standardowe | 5.98 |
| minimum | 1.00 |
| maksimum | 44.00 |
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Attendance
stat_desc <- data %>%
summarise(
średnia = mean(Attendance, na.rm = TRUE),
mediana = median(Attendance, na.rm = TRUE),
odchylenie_standardowe = sd(Attendance, na.rm = TRUE),
minimum = min(Attendance, na.rm = TRUE),
maksimum = max(Attendance, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Attendance"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Attendance | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 80.02 |
| mediana | 80.00 |
| odchylenie_standardowe | 11.59 |
| minimum | 60.00 |
| maksimum | 100.00 |
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Sleep_Hours
stat_desc <- data %>%
summarise(
średnia = mean(Sleep_Hours, na.rm = TRUE),
mediana = median(Sleep_Hours, na.rm = TRUE),
odchylenie_standardowe = sd(Sleep_Hours, na.rm = TRUE),
minimum = min(Sleep_Hours, na.rm = TRUE),
maksimum = max(Sleep_Hours, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Sleep_Hours"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Sleep_Hours | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 7.03 |
| mediana | 7.00 |
| odchylenie_standardowe | 1.48 |
| minimum | 4.00 |
| maksimum | 10.00 |
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Tutoring_Sessions
stat_desc <- data %>%
summarise(
średnia = mean(Tutoring_Sessions, na.rm = TRUE),
mediana = median(Tutoring_Sessions, na.rm = TRUE),
odchylenie_standardowe = sd(Tutoring_Sessions, na.rm = TRUE),
minimum = min(Tutoring_Sessions, na.rm = TRUE),
maksimum = max(Tutoring_Sessions, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Tutoring_Sessions"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Tutoring_Sessions | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 1.50 |
| mediana | 1.00 |
| odchylenie_standardowe | 1.24 |
| minimum | 0.00 |
| maksimum | 8.00 |
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Physical_Activity
stat_desc <- data %>%
summarise(
średnia = mean(Physical_Activity, na.rm = TRUE),
mediana = median(Physical_Activity, na.rm = TRUE),
odchylenie_standardowe = sd(Physical_Activity, na.rm = TRUE),
minimum = min(Physical_Activity, na.rm = TRUE),
maksimum = max(Physical_Activity, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Physical_Activity"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Physical_Activity | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 2.97 |
| mediana | 3.00 |
| odchylenie_standardowe | 1.03 |
| minimum | 0.00 |
| maksimum | 6.00 |
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Exam_Score
stat_desc <- data %>%
summarise(
średnia = mean(Exam_Score, na.rm = TRUE),
mediana = median(Exam_Score, na.rm = TRUE),
odchylenie_standardowe = sd(Exam_Score, na.rm = TRUE),
minimum = min(Exam_Score, na.rm = TRUE),
maksimum = max(Exam_Score, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Exam_Score"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)
| Statystyki Opisowe: | |
| Exam_Score | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 67.26 |
| mediana | 67.00 |
| odchylenie_standardowe | 3.90 |
| minimum | 56.00 |
| maksimum | 100.00 |
# Statystyki opisowe dla zmiennych ilościowych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
#. Macierz korelacji dla zmiennych ilościowych
macierz_korelacji <- cor(zmienne_ilosciowe, use = "complete.obs")
print(macierz_korelacji)
## Hours_Studied Attendance Sleep_Hours Previous_Scores
## Hours_Studied 1.000000000 -0.001527627 0.0126840091 0.017698977
## Attendance -0.001527627 1.000000000 -0.0185058862 -0.016306714
## Sleep_Hours 0.012684009 -0.018505886 1.0000000000 -0.015346396
## Previous_Scores 0.017698977 -0.016306714 -0.0153463956 1.000000000
## Tutoring_Sessions -0.013941975 0.014743286 -0.0091340906 -0.020365357
## Physical_Activity 0.005044221 -0.018809595 -0.0009687035 -0.005460835
## Exam_Score 0.413230008 0.550146082 -0.0099490753 0.161328016
## Tutoring_Sessions Physical_Activity Exam_Score
## Hours_Studied -0.013941975 0.0050442207 0.413230008
## Attendance 0.014743286 -0.0188095947 0.550146082
## Sleep_Hours -0.009134091 -0.0009687035 -0.009949075
## Previous_Scores -0.020365357 -0.0054608345 0.161328016
## Tutoring_Sessions 1.000000000 0.0151666001 0.136875188
## Physical_Activity 0.015166600 1.0000000000 0.036946720
## Exam_Score 0.136875188 0.0369467196 1.000000000
# Wizualizacja macierzy korelacji
corrplot(macierz_korelacji, method = "circle", type = "upper",
tl.col = "black", tl.srt = 45, col = colorRampPalette(c("blue", "white", "red"))(200))
dane_zwalidowane %>%
filter(Learning_Disabilities %in% c("Yes", "No")) %>%
ggbetweenstats(
y=Exam_Score,
x=Learning_Disabilities
)
dane_zwalidowane %>%
filter(Extracurricular_Activities %in% c("Yes", "No")) %>%
ggbetweenstats(
y=Exam_Score,
x=Extracurricular_Activities
)
set.seed(123)
gghistostats(
data = dane_zwalidowane,
x = Attendance,
title = "Wpływ frekwencji na wynik egzaminu",
test.value = 12,
binwidth = 1
)